# v_logsum

## PURPOSE V_LOGSUM v_logsum(x,d,k)=log(sum(k.*exp(x),d))

## SYNOPSIS function y=v_logsum(x,d,k)

## DESCRIPTION ```V_LOGSUM v_logsum(x,d,k)=log(sum(k.*exp(x),d))

Usage: (1) y=v_logsum(x) % log(sum(exp(x)))
(2) f=0.1*log(10); y=logsm(x*f)/f;  % add powers in dB

Inputs:  X(M,N,...) data matrix to sum
D          optional dimension to sum along [1st non-singular dimension]
K(M,N,...) optional scaling matrix. It must either be idential
in size to X, or else be a vector whose length is
equal to the size of dimension D of X

Outputs: Y(1,N,...) = log(sum(exp(X).*K,D))

This routine evaluates the given expression for Y but takes care to avoid
overflow or underflow.```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:
• v_gaussmixk V_GAUSSMIXK approximate Kullback-Leibler divergence between two GMMs + derivatives

## SOURCE CODE ```0001 function y=v_logsum(x,d,k)
0002 %V_LOGSUM v_logsum(x,d,k)=log(sum(k.*exp(x),d))
0003 %
0004 % Usage: (1) y=v_logsum(x) % log(sum(exp(x)))
0005 %        (2) f=0.1*log(10); y=logsm(x*f)/f;  % add powers in dB
0006 %
0007 % Inputs:  X(M,N,...) data matrix to sum
0008 %          D          optional dimension to sum along [1st non-singular dimension]
0009 %          K(M,N,...) optional scaling matrix. It must either be idential
0010 %                     in size to X, or else be a vector whose length is
0011 %                     equal to the size of dimension D of X
0012 %
0013 % Outputs: Y(1,N,...) = log(sum(exp(X).*K,D))
0014 %
0015 % This routine evaluates the given expression for Y but takes care to avoid
0016 % overflow or underflow.
0017
0018 %      Copyright (C) Mike Brookes 1998
0019 %      Version: \$Id: v_logsum.m 10865 2018-09-21 17:22:45Z dmb \$
0020 %
0021 %   VOICEBOX is a MATLAB toolbox for speech processing.
0023 %
0024 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0025 %   This program is free software; you can redistribute it and/or modify
0027 %   the Free Software Foundation; either version 2 of the License, or
0028 %   (at your option) any later version.
0029 %
0030 %   This program is distributed in the hope that it will be useful,
0031 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0032 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0033 %   GNU General Public License for more details.
0034 %
0035 %   You can obtain a copy of the GNU General Public License from
0036 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0037 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0038 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0039
0040 if nargin==1 || ~numel(d)
0041     d=[find(size(x)-1) 1];
0042     d=d(1);
0043 end
0044 n=size(x,d);
0045 if n<=1,            % use efficient computation if only one term in the sum
0046     if nargin<3
0047         y=x;
0048     else
0049         y=x+log(k);
0050     end
0051     return;
0052 end
0053 s=size(x);
0054 p=[d:ndims(x) 1:d-1];
0055 z=reshape(permute(x,p),n,prod(s)/n);
0056 q=max(z,[],1);              % we subtract y from each row to avoid dynamic range problems
0057 a=(q==Inf)|(q==-Inf);       % check for infinities
0058 if nargin<3
0059     y=q+log(sum(exp(z-q(ones(n,1),:)),1));
0060 elseif numel(k)==n
0061     y=q+log(sum(exp(z-q(ones(n,1),:)).*repmat(k(:),1,prod(s)/n),1));
0062 else
0063     y=q+log(sum(exp(z-q(ones(n,1),:)).*reshape(permute(k,p),n,prod(s)/n),1));
0064 end
0065 y(a)=q(a);                  % correct any column whose max is +-Inf
0066 s(d)=1;                     % update the dimension of the summed component
0067 y=ipermute(reshape(y,s(p)),p);
0068```